Singularity of Monomial Curves in A 3 and Gorenstein Monomial Curves in A 4

Source abstract

Let 2 ≦ s ∊ N and { n 1 , …, n s ) ⊆ N* . In 1884, J. Sylvester [13] published the following well-known result on the singularity degree S of the monomial curve whose corresponding semigroup is S : = 〈 n 1 , …, n s ): If s = 2, then Let K : = – Z \ S and for all 1 ≦ i ≦ s . We introduce the invariant of S involving a correction term to the Milnor number 2δ [4] of S . As a modified version and extension of Sylvester's result to all monomial space curves, we prove the following theorem: If s = 3, then We prove similar formulas for s = 4 if S is symmetric.